One of the important problems inherent in multi-carrier communication systems is a need to control and ultimately, to reduce the value of the peak-to-average power ratio (PAPR). Undesirably high amplitude values of the transmitted signal are typically caused by the closeness of phases of the components of input of the multi-tone transformation module (usually, the inverse discrete Fourier transform (IDFT)) of the transmitter. The solution to this problem should comprise a phase shifter that scrambles the data before they are converted into the transmitted broadband signal (e.g., OFDM or DMT symbol in commonly used multi-carrier systems). At the receiver, a phase deshifter should be applied accordingly. Gimlin and Patisaul (1993) consider the problem of phasing several equal-amplitude sinusoids and describe an optimal phase shifter that is due to Newman (1965). A similar phase shifter for a multi-carrier wireless communication system is described by Carney (1998). Another possible solution was proposed by May (1998) comprising an adaptive training of a communication system to reduce PAPR. Work on developing optimized phase shifters was also performed by Jafarkhani and Tarokh (2002).
Existing solutions usually comprise an “ultimate” phase shifter, i.e. a unique sequence that can be hard-coded. It is important to attain a general understanding of the structure of optimal phase shifters regardless of the specifics of the multi-tone transformation used. It is also important to develop an analytical foundation for easily generating such phase shifters for specific parameters of the multi-tone transformation.